Mechanic-elastic properties and radiation attenuation efficiency of TeO2/WO3/K2O composite glass systems for nuclear and medical application

WO3 effects on neutron and ionizing radiation defending factors of ternary tellurite-based glass blocks with molecular formula 80TeO2 –(20-x)WO3 – xK2O; x = 0–20 mol% (denoted as TKW-glass) has been reported via Phy-X theoretical calculations and Geant4 simulation code. Correlations between shielding factors and kinetics properties of the investigated glasses at different photon energy have been examined. The highest values of mass (MAC) attenuation coefficient were noted at 15 keV of the examined TKW-glass materials with the values of 38.408, 44.388, 49.855, 54.872, 59.492 cm2/g for TKW-0, TKW-5, TKW-10, TKW-15, and TKW-20, respectively. Generally, these values of the TKW-glasses obey the sequence: (TKW-0)MAC< (TKW-5)MAC < (TKW-10)MAC < (TKW-15)MAC < (TKW-20)MAC. The highest mean free path (MFP) values of TKW-glasses were registered at 15 MeV with the values of 6.101, 5.591, 5.097, 4.647, and 4.302 cm for TKW-0, TKW-5, TKW-10, TKW-15, and TKW-20, respectively. The two parameters half value layer (HVL) and MFP follow the pattern: (TKW-0)HVL, MFP > (TKW-5)HVL,MFP > (TKW-10)HVL,MFP > (TKW-15)HVL,MFP > (TKW-20)HVL,MFP. The maximum values of effective atomic number (EAN) took place at gamma energy of 15 keV corresponding to 44.35, 48.86, 52.63, 55.83, and 58.58 for TKW-0, TKW-5, TKW-10, TKW-15, and TKW-20, respectively. The trend of the buildup factors was similar for all of the glass specimens. The fast neutron removal cross-section (ΣR) enhanced as WO3 content increased in the specimens. Thus, the peaked value of ΣR is 0.1059 cm−1 was noted in the TKW-20 sample. Mechanical properties, neutron and γ-rays protection parameters were observed to improve with enhanced WO3 mol% in the TKW-glasses. The current results bear their utilization for neutron and gamma protection purposes.

.86, 52.63, 55.83, and 58.58 for TKW-0, TKW-5, TKW-10, TKW-15, and TKW-20, respectively. The trend of the buildup factors was similar for all of the glass specimens. The fast neutron removal cross-section (Σ R ) enhanced as WO 3 content increased in the specimens. Thus, the peaked value of Σ R is 0.1059 cm − 1 was noted in the TKW-20 sample. Mechanical properties, neutron and γ-rays protection parameters were observed to improve with enhanced WO 3 mol% in the TKW-glasses. The current results bear their utilization for neutron and gamma protection purposes.

Introduction
According to modern technology, it is noted that natural and artificial ionizing radiation such as γ-and X-rays sources and their radio-isotopes were applied in extremely in several functions especially in radiotherapy and nuclear medical area. In the other side, in nuclear reactors, fissionable radionuclides are applied to produce isotopes generation and electric power. Guaranteed sources of 201 Tl, 123 I, and 60 Co are isotopes applied in medical field for sterilizing medical equipment, and as nuclear medicine. Moreover, ionized-rays beams may be used in food handling, protection, and for examining physical and chemical material characterizations.
Regardless of the great advantages of these radiant sources, it is accompanied by some harmful effects for human and environment. Consequently, looking for appropriate shields as a radiation protection becomes critical goal for several scientific researchers, investigators, and engineers. Therefore, the field of nuclear protection as an essential tool in technology is promising. Choosing materials for this aim is mainly controlled by several parameters such as available space, radiation source strength and excellence, preparation charge, required optical, physic-mechanic, and thermal description of the protection place. In the area of radiation shielding, neutrons, photon beams are of main concern due to their highest diffusivity. Thus, shield factors for these types of radiation are necessary when in evaluation process for any material as ionizing radiation shield.
This article deals with the mechanical features of 80TeO 2 -(20-x)WO 3 -xK 2 O: x = 0-20 mol% (TKW-glasses). We also present more detail for neutron and gamma shield factors of the TKW-glasses. The MAC, HVL, MFP, LAC, and TVL have been reported. In addition, correlations between shielding factors and the kinetics features of the studied glassy materials at diverse photons energy were examined.

Description of samples
Five of tellurite-based glass systems with chemical composition 80TeO 2 -(20-x)WO 3 -xK 2 O: x = 0-20 mol% (in steps of 5 mol%) were adapted from Ref. [30] to perform the aim of the present research. The investigated glass samples were prepared via melt quenching route. The mixture of each sample (according to Table 1) was preheated at 400 • C, and then melted at 800 • C-1000 • C for 30 min. The produced samples were annealed at the glass transition temperature for each glass sample for 60 min. In the current study, the investigated glasses are coded as: TKW-0: 80TeO 2 -0.0WO 3 -20K 2 O with density 4.500 (g/cm 3 ). TKW-5: 80TeO 2 -5WO 3 -15K 2 O with density 4.766 (g/cm 3 ).

Gamma-ray attenuation parameters
The incident (I o ) and transmitted (I) gamma-ray intensity, material's thickness (t) as well as linear attenuations coefficients (LAC = μ) are connected via the Beer-Lambert law as in equation (1) [ [34][35][36][37][38]: with the help of the calculated μ and measured (ρ) of the Fe-glasses, the mass attenuations coefficients (MAC = μ m ) of the samples can be calculated via equation (2): The total MAC for a composite material is given as the mixing rule as in equation (3) [34-38]: where wi and (μ/ρ)i are the weight fractions and the mass attenuation coefficient (MAC) values of the ith element, respectively. The Phys-X/PSD program was used to evaluate the half-value-layer radiation shielding parameters, mean free path (MFP), tenth value layer (TVL) and Effective atomic number (Z eff ) as in equations (4)-(7) [36]:  More details on the mechanical features of these glasses as well as all of the radiation shielding properties were assessed as described elsewhere [30,[34][35][36][37][38].  Fig. 2) and then the simulations repot was confirmed via Phys-X theoretical calculations. All the numerical values of MAC obtained from Geant4 and Phy-X platforms are summarized in Table 2 and Table 3. Obviously, an excellent agreement between both approaches has been revealed. Table 4 shows a comparison of linear (LAC) attenuation coefficient values for the sample named as TKW-20 with some commercial radiation shielding materials (glasses and concrete) such as S1: 25BaO-10Fe 2 O 3 -10Na 2 O-55V 2 O 5 [39], S2: [41], S4: 10Na 2 CO 3 -50H 3-BO 3 -10ZnO-20SiO 2 -10BaO [42], S5: Ordinary concrete (OC) [43], S6: Hematite-Serpentine concrete (HSC) [43], RS-253-G18 [44], RS-360 [44], and RS-520 [44]. As shown in Table 4, the investigated TKW-20 sample possessed the highest LAC values compared to all        other samples. Therefore, TKW-20 sample has high capacity for radiation shielding compared to other studied glasses (S1, S2. S3. S4, and S5) and concrtete (OC and HSC), and commercial glasses (RS-253-G18, RS-360, and RS-520). Fig. 3 describes the trend of HVL values as a function of γ-photons energies for unlike concentrations of WO 3 content. Generally, HVL values enlarged as a function of photonic energies. This implies that as photons become more energetic, they become highly penetrating the glass sample, so more thickness of glass is needed to absorb them. Also, the HVL values are inversely to MAC, then, highest values of HVL were obtained for TKW-0 sample, because it has the least density due to lower WO 3 content. Fig. 4 describes the MFP performance as an increment of the incident γ-photon energies for TKW-glasses. The highest MFP values of the studied TKWglasses have been seen at 15 MeV, the corresponding HVL are 6.101, 5.591, 5.097, 4.647, and 4.302 cm for TKW-0, TKW-5, TKW-10, TKW-15, and TKW-20, respectively.

Results and discussion
Another important term to signify the radiation-security capacity of the tested TKW-glassy materials is the effective atomic number denoted as EAN or Z eff . , and TKW-20, respectively. Moreover, the term of effective electron density (denoted as EED or N eff ) can be calculated directly by using the EAN values. Fig. 6 describes the performance of EED (N eff ) versus the gamma-photons energies for different concentrations of WO 3 content. From Fig. 6, the values of (N eff ) increase as the concentration of WO 3 increases in the glass structure. This is because of (Z eff ) and (N eff ) of sample mainly depends on its atomic number. Therefore, (Z eff ) and (N eff ) followed the trend: (Z eff , N eff ) TKW-20 > (Z eff , N eff ) TKW-15 > (Z eff , N eff ) TKW-10 > (Z eff , N eff ) TKW-5 > (Z eff , N eff ) TKW-0 .
The determination of the calculated equivalent atomic number (Z eq ) serves as an initial step in assessing the buildup factors of composite-based glasses. Z eq values were computed for the investigated TKW-glasses across a broad energy spectrum 0.015 < E < 15.0 MeV. In Fig. 7, the variations in equivalent atomic number (Zeq) are illustrated as a function of γ-photonic energy for TKW-glass systems. Notably, Z eq undergoes changes in three distinct energy realms, corresponding to partial photons-matter interactions. Additionally, a prominent peak is observed in close proximity to the k-absorption edge of the 52 Te 128 , attributed to the photoelectric effect. Beyond this peak, Z eq experiences a gradual increase with rising γ-photon energy up to 1.0 MeV, followed by a significant   Table 5. From this table, Σ R increased as WO 3 content increased in the glass specimens. Therefore, the highest Σ R value of 0.1059 cm − 1 was recorded for TKW-20 sample.
Regarding to the physical properties of the proposed TKW-glasses as shown in Tables 1 and it is obvious that the glass density increases from 4.500 g/cm 3 for TKW-0 to 5.766 g/cm 3 for TKW-20 glass as WO 3 content increases from 0 to 20 mol%. On the other hand the V m reduced from 32.6 to 3.2 cm 3 /mol. These two physical changes of TKW-glass systems are attribute to the replacement of K 2 O by WO 3 in accordance of possible interchange of the atomic radii 2.20 and 1.35 A o and atomic masses 39.98 and 183.84 of potassium and tungsten, respectively [30]. The influence of WO 3 on the elastic moduli (e.g., Y, E, and K) and microhardness (H) of the TKW-glasses was studied formerly in Ref. [30], where these parameters have been found to increase as WO 3 -content as shown in Table 6.
In addition, as shown in the present work that gamma-ray shielding parameters (HVL, MFP, ect.) were improved with the increase  of WO 3 content. Finally, correlations between mechanical and radiations-shielding possessions of the TKW-glasses are studied, Fig. 11 (a-d) depict the variant of MAC with young's modulus (E), while the variation of tenth value layer (TVL) with bulk modulus (K) is shown in Fig. 12(a-d) at four selected photon energy (e.g., E = 0.015, 0.1, 10 and 10 MeV) as in Table 7. From Figs. 11 and 12, we noted that the MAC leveled up as a function Young's modulus, while the TVL parameter decrease with increasing bulk modulus at different photon energies of the TKW-glass systems with the raise of WO 3 molar concentrations. The dependence of the EBF parameter on micro-hardness factor of the TKW-0 glasses at mpf = 1, 10, 20, and 40 mfp at different photonic energy E = 0.015, 1.5, and 15.0 MeV is illustrates in Fig. 13(a-c), and Table 8. It is seen that the EBF factor decreases with the increasing of micro-hardness parameter at low photon energies as in Fig. 13a and b, while it increases at high photon energy as in Fig. 13c. Fig. 14 shows the deviation of FNRCS values (for fast neutron) versus the bulk modulus of the current TKW-glasses, it is clear that this parameter enhances with the increasing of bulk modulus for glasses. These results confirm the main role of WO 3 on the mechano-radio-shielding features of the investigated TKW-glasses pinpointed to their utilization neutron and gamma shield purposes.

Conclusion
The article presents the influence of WO 3 on neutron and ionizing radiation shielding factors of ternary tellurite-based glassy materials containing WO 3 and K 2 O. Correlations between shielding factors and the mechano-elasto features of the examined glass series at different photon energy were examined. The following outcomes are noted.